Title:  Compressible Navier-Stokes equations with temperature dependent dissipation

Abstract:  From its physical origin, the viscosity and heat conductivity coe!cients in compressible fluids depend on absolute temperature through power laws. The mathematical theory on the well-posedness and regularity on this setting is widely open. I will report some recent progress on this direction, with emphasis on the lower bound of temperature, and global existence of solutions in one or multiple dimensions. The relation between thermodynamics laws and Naiver-Stokes equations will also be discussed. This talk is based on joint works with Weizhe Zhang.